Surface effects in Debye screening

A thermodynamic system of equally charged, plus and minus, classical particles constrained to move in a (spherical) ball is studied in a region of parameters in which Debye screening takes place. The activities of the two charge species are not taken as necessarily equal. We must deal with two physically interesting surface effects, the formation of a surface charge layer, and long range forces reaching around the outside of the spherical volume. This is an example in as much as 1) general charge species are not considered, 2) the volume is taken as a ball, 3) a simple choice for the short range forces (necessary for stability) is taken. We feel the present system is general enough to exhibit all the interesting physical phenomena, and that the methods used are capable of extension to much more general systems. The techniques herein involve use of the sine-Gordon transformation to get a continuum field problem which in turn is studied via a multi-phase cluster expansion. This route follows other recent rigorous treatments of Debye screening.